MinT - Best Known (45, 45+65, s)-Nets in Base 16

Best Known (45, 45+65, s)-Nets in Base 16

(45, 45+65, 225)-Net over F₁₆ — Constructive and digital

Digital (45, 110, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 110, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(45, 45+65, 242)-Net over F₁₆ — Digital

Digital (45, 110, 242)-net over F₁₆, using

net from sequence [i] based on digital (45, 241)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 45 and N(F) ≥ 242, using
  - a curve from the manYPoints database [i]

(45, 45+65, 10755)-Net in Base 16 — Upper bound on s

There is no (45, 110, 10756)-net in base 16, because

1 times m-reduction [i] would yield (45, 109, 10756)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 177962 839448 685401 026152 638861 858135 489970 387626 807190 554349 159783 620959 164269 473298 107098 858395 912404 318188 314740 300384 860201 255856 > 16¹⁰⁹ [i]